question_answer

The area of the largest triangle that can be inscribed in a semicircle of radius r cm is?

A) \[2\,\,r\,\,c{{m}^{2}}\]             

B) \[{{r}^{2}}\,\,c{{m}^{2}}\]

C) \[\frac{1}{2}{{r}^{2}}\,\,c{{m}^{2}}\]                      

D) \[2{{r}^{2\,}}\,\,c{{m}^{2}}\]

Correct Answer: B

Solution :

Let \[\Delta \]ABC is a largest triangle in a semi circle Then, Area of \[\Delta ABC\]=\[\frac{1}{2}\times AB\times CD\] \[=\frac{1}{2}\times 2r\times r\] \[={{r}^{2}}c{{m}^{2}}\]